plumiSimultaneous equations: OCR MEI A‑Level Maths questions
OCR MEI A-Level Maths past-paper questions on 2.4 Simultaneous equations, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 15 questions on Simultaneous equations, as a list
- June 2025, Paper 1, Q8 (7 marks): (a) Determine the two values of k for which the line y x 3 + is a tangent to the curve 5 = x2 y k kx [4] . = - - x2 (b) These values of k are used to define two
- June 2024, Paper 1, Q15 (9 marks): 2 15 The circle x y 2 x 14 y 25 0 has its centre at the point C. The line y 7 x 25 intersects + + - + = = + the circle at points A and B. Prove that triangle AB
- June 2024, Paper 3, Q15 (6 marks): 15 (a) Show that, for the curve y ax bx + , the equation of the tangent at the point with c = + 2 x‑coordinate t is y ( 2 at b x ) at + . c [3] = + - 2 (b) Henc
- June 2024, AS Paper 1, Q8 (10 marks): 2 8 A circle with centre C has equation x y 6 x 16 y 48 0 . + - - + = (a) Find the coordinates of C. [2] A line has equation y x - and intersects the circle at
- June 2024, AS Paper 2, Q8 (4 marks): In this question you must show detailed reasoning. Determine the coordinates of the point of intersection of the line with equation y 2 x + and the 3 = 2 2 curv
- June 2023, Paper 1, Q7 (7 marks): Determine the exact distance between the two points at which the line through (4, 5) and (6, -1) 2 meets the curve y 2 x 7 x + . 1 [7] = -
- June 2023, AS Paper 1, Q8 (9 marks): In this question you must show detailed reasoning. 2 2 (a) Find the centre and radius of the circle with equation x y 2 x 4 y 20 0 . [4] + - + - = (b) Find the
- June 2022, AS Paper 2, Q7 (7 marks): (a) On the pair of axes in the Printed Answer Booklet, sketch the graphs of • y 2 x 4 = + 2 • y [2] = x (b) Determine the x-coordinates of the points of interse
- November 2021, Paper 1, Q7 (10 marks): In this question you must show detailed reasoning. The points A (-1, 4) and B (7, -2) are at opposite ends of a diameter of a circle. (a) Find the equation of t
- November 2021, Paper 3, Q3 (7 marks): (a) Determine, in terms of k, the coordinates of the point where the lines with the following equations intersect. x y k + = [3] 2 x y 1 - = (b) Determine, in t
- November 2021, AS Paper 1, Q1 (2 marks): Find the coordinates of the point of intersection of the lines y 3 x - and 2 x 2 y 10 . [2] = + =
- November 2021, AS Paper 1, Q5 (5 marks): The diagram shows the triangle ABC in which AC 13 cm and AB is the shortest side. The = 4 perimeter of the triangle is 32 cm. The area is 24cm2 and sinB . = 5 A
- November 2021, AS Paper 1, Q9 (9 marks): (a) Sketch both of the following on the axes provided in the Printed Answer Booklet. 12 (i) The curve y , stating the coordinates of at least one point on the c
- November 2020, AS Paper 2, Q7 (8 marks): In this question you must show detailed reasoning. A circle has centre (2, - 1) and radius 5. A straight line passes through the points (1, 1) and (9, 5). Find
- June 2018, Paper 3, Q7 (8 marks): In this question you must show detailed reasoning. 2 Fig. 7 shows the curve y 5 x x . = - y x O Fig. 7 2 The line y kx crosses the curve y x x on the x-axis and
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